Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together? (a) 10, (b) 16, (c) 9, (d) 15

Calculation:

A least common multiple of (2, 4, 6, 8, 10 and 12)

we can write 2 = 1 × 2

4 = 22

6 = 2 × 3

8 = 23

10 = 2 × 5

12 = 22 × 3

A least common multiple of (2, 4, 6, 8, 10 and 12) = 23 × 3 × 5

⇒ 8 × 3 × 5

⇒ 120 sec

Bells ring together after every 120 sec

Required number of times in 30 minutes (30 × 60 seconds ) = [(30 × 60)/120]

⇒ 15

But we have to add 1 because at the start all bells will be rung once a time after that they ring 15 times.

⇒ 15 + 1

⇒ 16 times

Summary:

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, and 12 seconds respectively. In 30 minutes, how many times do they toll together? (a) 10, (b) 16, (c) 9, (d) 15

Six bells start off ringing simultaneously and ring every 2, 4, 6, 8, or 10 seconds. They chime 16 times together in 30 minutes.